Lithium battery electrochemical thermal coupling model parameter sensitivity quantification and optimization method

Abstract

The invention relates to the field of design, optimization and application of a lithium ion battery simulation model, and discloses a lithium battery electrochemical thermal coupling model parameter sensitivity quantification and optimization method, which comprises the following steps: constructing an electrochemical thermal coupling model of a lithium battery; adopting Latin hypercube sampling and Sobol global sensitivity analysis methods to obtain the sensitivity of each parameter under a preset working condition; selecting a core optimization parameter group from the plurality of parameters according to a preset working condition; aiming at the core optimization parameter group of the preset working condition, optimizing by adopting a non-dominated sorting genetic algorithm to obtain a comprehensive performance optimal solution; and constructing a general parameter combination according to the comprehensive performance optimal solution under various preset working conditions. According to the method, Latin hypercube sampling and Sobol global sensitivity analysis are combined, quantitative evaluation is performed on the electrochemical-thermal coupling model parameters of the lithium battery, core parameters having key influences on model output under different working conditions can be identified, and the problem of one-sided local sensitivity analysis results is avoided.

Description

Technical Field

[0001] This invention relates to the field of lithium-ion battery simulation model design, optimization and application, and in particular to a method for quantifying and optimizing the parameter sensitivity of a lithium battery electrochemical-thermal coupling model. Background Technology

[0002] Lithium-ion batteries, due to their advantages such as high energy density, long cycle life, low self-discharge rate, and environmental friendliness, have been widely used in new energy vehicles, energy storage power stations, and portable electronic devices. In actual operation, lithium-ion batteries undergo complex electrochemical reactions and heat transfer processes during charging and discharging. Their internal potential distribution, ion concentration changes, and temperature evolution behavior exhibit significant nonlinear and strongly coupled characteristics, and they are highly sensitive to operating current, ambient temperature, and operating conditions. Therefore, establishing an electrochemical-thermal coupling model that accurately describes the battery's electrochemical behavior and thermal response characteristics is of great significance for battery performance analysis, state estimation, and thermal safety management.

[0003] Currently, electrochemical-thermal coupled models, combining electrochemical and thermal models based on porous electrode theory, have become an important tool for modeling the mechanism and predicting the performance of lithium-ion batteries. However, these models typically involve a large number of parameters, including geometric, capacity, transport, kinetic, and thermodynamic parameters, the rationality and accuracy of which have a decisive impact on the model's output. Due to the complexity of the battery's internal structure, the multi-scale coupling of physicochemical processes, and limited experimental measurement conditions, these parameters are often difficult to obtain accurately through direct experiments and are easily affected by differences in manufacturing processes, aging states, and environmental conditions, leading to reduced model prediction accuracy. Therefore, conducting sensitivity analysis and optimization calibration of model parameters is a crucial step in improving model accuracy and engineering applicability.

[0004] Existing research on lithium-ion battery model parameter optimization largely focuses on model structure improvement, local parameter sensitivity analysis, or parameter calibration under single operating conditions. Some studies employ local sensitivity analysis to assess the impact of parameters on model output; however, these methods are typically based on small perturbations of parameters near a baseline, making it difficult to reflect the true impact of parameters across the entire value range and their interactions on model output. Furthermore, existing research often emphasizes electrochemical reaction-related parameters in parameter selection, neglecting the systematic consideration of geometric structural parameters, transport parameters, and thermodynamic parameters. This results in incomplete identification of sensitive parameters, hindering effective guidance for overall model optimization. Moreover, current sensitivity analysis and parameter optimization efforts are mostly based on single static operating conditions such as constant rate, failing to fully consider the changing characteristics of model parameter sensitivity under dynamic rate conditions, automotive operating conditions, and different depths of discharge and ambient temperatures. Consequently, the optimized parameter combinations exhibit poor adaptability under complex real-world operating conditions.

[0005] On the other hand, existing model parameter optimization methods typically focus on single performance indicators such as terminal voltage prediction accuracy or temperature rise control in their target setting, lacking synergistic consideration of electrochemical performance and thermal safety performance. This makes it difficult to achieve a balanced improvement in the overall model performance under conditions of conflicting objectives. Furthermore, existing technologies lack effective integration between sensitivity analysis and parameter optimization, failing to construct targeted optimization strategies for the differences in sensitive parameters under different operating conditions. Often, the model is optimized independently only under a single operating condition, leading to parameter redundancy, low optimization efficiency, and difficulty in achieving unified model adaptation under multiple operating conditions. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to overcome the shortcomings of the prior art and provide a method for quantifying and optimizing the sensitivity of parameters in a lithium battery electrochemical thermocoupled model.

[0007] This invention is achieved through the following technical solution:

[0008] A method for quantifying and optimizing the sensitivity of parameters in a lithium battery electrochemical-thermal coupling model, comprising the following steps:

[0009] S1, Construct an electrochemical-thermal coupling model for lithium batteries;

[0010] S2, using Latin hypercube sampling and Sobol global sensitivity analysis, the parameters of the electrochemical thermocoupled model are subjected to global sensitivity quantification analysis to obtain the sensitivity of each parameter under preset operating conditions;

[0011] S3, based on the sensitivity of each parameter under preset working conditions, select a core optimization parameter group from multiple parameters for the preset working conditions;

[0012] S4. For the core optimization parameter set of the preset working condition, the non-dominated sorting genetic algorithm is used for optimization to generate a Pareto solution set with the dual objectives of minimizing terminal voltage error and temperature rise error. The Pareto solution set is then screened using the minimum Euclidean distance method, and the parameter set with the smallest distance to the ideal target point is selected as the optimal solution for the overall performance of the preset working condition.

[0013] S5 constructs a general parameter combination based on the optimal comprehensive performance solution under various preset working conditions.

[0014] Preferably, step S1 includes the following steps:

[0015] The electrochemical-thermal coupling model includes a geometric field, a capacity field, a transport field, a kinetic field, and a thermodynamic field.

[0016] Preferably, step S1 further includes the following step:

[0017] Based on the simulation results output by the electrochemical thermocoupled model under preset operating conditions and the experimental results under the same operating conditions, the deviation between the simulation results and the experimental results is calculated.

[0018] The electrochemical thermocoupled model is modified under the constraint that the deviation does not exceed a preset threshold.

[0019] Preferably, step S2 includes the following steps:

[0020] Obtain the ratio of the partial variance to the total variance of the electrochemical-thermal coupling model for multiple discharge depths under preset operating conditions;

[0021] The mean of the normalized first-order effect index of the parameter is determined based on multiple ratios.

[0022] The sensitivity category of the parameter under preset operating conditions is determined based on the mean value.

[0023] Preferably, "determining the sensitivity category of the parameter under preset operating conditions based on the mean value" includes the following steps:

[0024] When the mean value is greater than the first preset value, the sensitivity category of the parameter is high sensitivity;

[0025] When the mean value is less than a first preset value and greater than a second preset value, the sensitivity category of the parameter is moderately sensitive.

[0026] When the mean value is less than the second preset value and greater than the third preset value, the sensitivity category of the parameter is low sensitivity;

[0027] When the mean is less than a third preset value, the sensitivity category of the parameter is insensitive.

[0028] The first preset value is greater than the second preset value, and the second preset value is greater than the third preset value.

[0029] Preferably, the preset operating conditions include a 1C constant rate discharge condition at 25°C, a 0.5C-1C-2C dynamic rate discharge condition, and a dynamic stress test cycle vehicle operating condition.

[0030] Preferably, step S4 includes the following steps:

[0031] Based on the simulation and experimental results of the optimal solution for overall performance under preset operating conditions, determine whether it is necessary to optimize the optimal solution for overall performance.

[0032] Preferably, step S5 includes the following steps:

[0033] Based on the simulation and experimental results of the general parameter combination, determine whether the general parameter combination needs to be optimized.

[0034] The beneficial effects of this invention are:

[0035] This invention combines Latin hypercube sampling with Sobol global sensitivity analysis to quantitatively evaluate the influence of lithium battery electrochemical-thermal coupling model parameters across the entire parameter space and their interactions. This comprehensively and accurately identifies core parameters that significantly impact model output under different operating conditions, avoiding the one-sided results of local sensitivity analysis in existing technologies. Furthermore, it constructs core optimization parameter sets only for highly sensitive parameters and introduces a non-dominated sorting genetic algorithm to conduct multi-objective collaborative optimization of terminal voltage error and temperature rise error. This significantly reduces parameter redundancy, improves optimization efficiency, and achieves a comprehensive balance between electrochemical performance and thermal safety performance. Moreover, by fusing optimal solutions from multiple operating conditions to construct a universal parameter combination, the established electrochemical-thermal coupling model exhibits higher prediction accuracy and adaptability under dynamic rate of change, different temperatures, and complex actual operating conditions, thereby significantly enhancing the model's engineering practical value and reliability.

[0036] Furthermore, by constructing an electrochemical-thermal coupled model that simultaneously encompasses the geometric, capacity, transport, kinetic, and thermodynamic fields, this invention can provide a unified description of the lithium battery operation process from multiple levels, including structural characteristics, charge and mass transport behavior, electrochemical reaction kinetics, and heat generation and transfer mechanisms. This achieves comprehensive coupled modeling of the battery's internal electrochemical behavior and temperature evolution, thereby significantly improving the model's accuracy in characterizing voltage response and temperature rise changes under actual operating conditions. This provides a physically consistent and highly complete model foundation for subsequent parameter sensitivity analysis and multi-objective optimization, which is beneficial for improving the reliability and engineering applicability of the model analysis results.

[0037] Furthermore, by introducing a quantitative calculation of the deviation between the simulation results and the corresponding experimental results in step S1, and using the deviation not exceeding a preset threshold as a constraint to correct the electrochemical-thermal coupling model, this invention can realize the verification and self-consistent adjustment of the model's effectiveness during the model construction stage, avoiding the introduction of systematic errors due to unreasonable initial model settings, thereby significantly improving the model's fit and credibility to real battery behavior. This approach provides a basic model with controllable errors and stronger physical consistency for subsequent parameter sensitivity analysis and multi-objective optimization, which is conducive to improving the stability, accuracy, and reliability of optimization results in practical engineering applications.

[0038] Furthermore, this invention introduces the calculation of the ratio of the partial variance to the total variance of parameters under different discharge depths under preset operating conditions in step S2, and determines the mean of the normalized first-order effect index based on this ratio to classify parameter sensitivity categories. This invention can systematically characterize the overall influence of model parameters in the full discharge process, avoiding the one-sidedness of evaluating parameter sensitivity only at a single discharge depth or under local conditions. This method effectively reduces the interference of instantaneous operating condition fluctuations on the sensitivity analysis results, making the sensitive parameter identification results more stable and representative, thereby providing a more objective and reliable basis for the selection of core optimization parameters, which is conducive to improving the pertinence of subsequent parameter optimization and the accuracy of model prediction.

[0039] Furthermore, this invention compares the mean of the normalized first-order effect index of the parameters with multiple preset thresholds set in a hierarchical manner, and classifies the parameter sensitivity into four categories: high sensitivity, moderate sensitivity, low sensitivity, and insensitivity. This invention can distinguish the degree of influence of different parameters on the model output in a clear, quantitative, and comparable way, avoiding the problem of traditional sensitivity analysis that only provides numerical values ​​without the lack of engineering judgment criteria. This hierarchical mechanism helps to highlight key high-sensitivity parameters, reasonably retain moderately sensitive parameters, and effectively eliminate low-sensitivity and insensitivity parameters in the subsequent parameter screening and optimization process, thereby reducing parameter dimensionality, reducing computational complexity, and improving optimization efficiency, while improving the rationality of model parameter configuration and the operability of engineering applications.

[0040] Furthermore, by setting preset operating conditions including a constant 1C discharge condition at 25°C, a dynamic 0.5C-1C-2C discharge condition, and a dynamic stress test cycle vehicle operating condition, this invention can analyze and optimize the parameters of the electrochemical-thermal coupling model under a combination of typical static and complex dynamic operating conditions. This covers both standard test scenarios commonly used in laboratories and the actual operating conditions in practical applications such as new energy vehicles, thereby comprehensively reflecting the sensitivity differences of model parameters under different load changes and operating condition switching conditions. This setting effectively improves the adaptability and robustness of the selected parameters and optimization results to actual operating conditions, making the constructed model more versatile and reliable in engineering applications. Attached Figure Description

[0041] Figure 1 This is a flowchart of a method for quantifying and optimizing the sensitivity of parameters in a lithium battery electrochemical-thermal coupling model, as described in this invention.

[0042] Figure 2 This is a schematic diagram of the electrochemical-thermal coupling model of the lithium-ion battery of the present invention;

[0043] Figure 3This is a comparison chart of the simulation results curve and the experimental results curve of the terminal voltage of the electrochemical thermal coupling model under the 1C constant rate discharge condition at 25℃ according to the present invention.

[0044] Figure 4 This is a comparison of the simulation results curve and the experimental results curve of the temperature rise of the electrochemical thermal coupling model under the constant discharge rate of 1C at 25℃ in this invention.

[0045] Figure 5 This is a parameter sensitivity result diagram of the present invention under the 1C constant rate discharge condition at 25°C;

[0046] Figure 6 This is a parameter sensitivity result diagram of the present invention under the dynamic rate discharge conditions of 0.5C-1C-2C;

[0047] Figure 7 This is a graph showing the parameter sensitivity results of the dynamic stress test under cyclic vehicle operating conditions according to the present invention;

[0048] Figure 8 This is a schematic diagram of the parameter allocation results of the hierarchical division of labor parameter optimization strategy of the present invention;

[0049] Figure 9 This is a comparison of the simulation results curve and the experimental results curve of the terminal voltage of the optimized electrochemical thermal coupling model under the 1C constant rate discharge condition at 25℃ according to the present invention.

[0050] Figure 10 This is a comparison of the simulation results curve and the experimental results curve of the temperature rise of the optimized electrochemical thermal coupling model under the 1C constant rate discharge condition at 25℃ according to the present invention.

[0051] Figure 11 This is a comparison of the simulation results curve and the experimental results curve of the terminal voltage of the electrochemical thermocoupled model under the optimized 0.5C-1C-2C dynamic rate discharge condition of the present invention.

[0052] Figure 12 This is a comparison of the simulation results and experimental results of the temperature rise of the optimized electrochemical-thermal coupling model under the 0.5C-1C-2C dynamic rate discharge condition according to the present invention.

[0053] Figure 13 This is a comparison chart of the simulation results curve and the experimental results curve of the terminal voltage of the optimized dynamic stress test cycle vehicle operating condition electrochemical thermocoupled model of the present invention.

[0054] Figure 14 This is a comparison chart of the simulation results curve and the experimental results curve of the temperature rise of the optimized dynamic stress test cycle electrochemical thermocoupled model of the present invention under vehicle working conditions.

[0055] Figure 15 These are the terminal voltage error effect diagrams before and after optimization under three preset working conditions of the present invention;

[0056] Figure 16 These are the temperature rise error effect diagrams before and after optimization under three preset working conditions of the present invention;

[0057] Figure 17 This is a comparison of the terminal voltage curves before and after optimization under the 1C constant rate discharge condition at 25°C according to the present invention.

[0058] Figure 18 This is a comparison of the temperature rise curves before and after optimization under the 1C constant rate discharge condition at 25℃ according to the present invention. Detailed Implementation

[0059] To enable those skilled in the art to better understand the technical solutions of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and preferred embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0060] This invention provides a method for quantifying and optimizing the parameter sensitivity of a lithium battery electrochemical-thermal coupling model, the method comprising the following steps:

[0061] S1. Constructing an electrochemical-thermal coupling model for lithium-ion batteries. This model is specifically built using COMSOL Multiphysics simulation software. The electrochemical-thermal coupling model combines the electrochemical and heat transfer processes within the lithium-ion battery to accurately simulate the distribution and changes in current, potential, and temperature during charging and discharging. Specifically, based on the pseudo-two-dimensional electrochemical model theory (P2D theory), partial differential equations are used to accurately describe the electrochemical reaction processes within the lithium-ion battery. The model details the concentration trends of the solid and liquid phases, the potential distribution patterns of the solid and liquid phases, the reaction kinetics at the solid / liquid interface, and the impact of temperature changes on the battery model output and parameters. A schematic diagram of the electrochemical-thermal coupling model is available in [link to schematic diagram]. Figure 2 .

[0062] The electrochemical model of the electrochemical-thermal coupling model includes the following equations:

[0063] The equation for lithium ion concentration distribution in solid particles. The diffusion equation of lithium ions in solid spherical particles is described by Fick's Second Law of Diffusion in spherical coordinates.

[0064]

[0065] In the formula, c s (x,r,t) represents the lithium-ion concentration at time t at the x-coordinate along the battery thickness and the r-coordinate along the radial direction; D s This represents the diffusion coefficient of lithium ions in solid particles.

[0066] Solid-phase potential distribution equation. The solid-phase potential distribution at the electrode is described using a charge conservation equation based on Ohm's law:

[0067]

[0068] In the formula, i s (x,t) represents the solid current density at coordinate x; σ eff φ is the effective conductivity of the electrode solid phase; s (x,t) represents the solid-state potential at coordinate x.

[0069] The equation for lithium ion concentration distribution in the liquid phase. Mass transfer in the liquid phase can be described by the Nernst–Planck equation, and the specific lithium ion concentration distribution in the liquid phase is shown in the following equation:

[0070]

[0071] In the formula, ε e c is the liquid volume fraction; e (x,t) represents the liquid lithium-ion concentration at coordinate x; t + D is the lithium-ion transference number. effe a is the effective diffusion coefficient of lithium ions in the liquid phase; s denoted as the average specific surface area of ​​the active particles.

[0072] Liquid phase potential distribution equation. According to Ohm's law and McInnes' equation, the potential distribution equation for the liquid electrolyte is:

[0073]

[0074] In the formula, i e (x,t) represents the liquid current density at coordinate x at time t; φ e (x,t) represents the liquid phase potential at coordinate x; R is the ideal gas constant; F is the Faraday constant; κ eff This represents the effective conductivity of liquid-phase ions.

[0075] Solid / liquid interface reaction kinetics equation. Based on the Butler–Volmer kinetic equation, the relationship between lithium-ion pore wall flux at the solid / liquid interface and the reaction overpotential at the solid / liquid interface is as follows:

[0076]

[0077] In the formula, α is the electrochemical reaction transfer coefficient; i0(x,t) is the exchange current density, which can be obtained by the following formula:

[0078]

[0079] In the formula, k eff η is the effective rate constant for the electrochemical reaction; η(x,t) represents the overpotential of the reaction, and η(x,t) can be expressed as:

[0080] η(x,t)=φ s (x,t)-φ e (x,t)-U ocv -FR SEI j(x,t)

[0081] In the formula, R SEI U represents the membrane resistance of the solid electrolyte interphase (SEI) membrane on the surface of solid particles; ocv It represents the thermodynamic equilibrium potential.

[0082] The final output characteristic of the battery, namely the terminal voltage, is calculated from the solid-phase potential difference between the positive and negative electrodes:

[0083]

[0084] The thermodynamic model equations of the electrochemical-thermal coupling model are as follows:

[0085] The heat conduction equation, based on Fourier's law, describes the change of the temperature field with time during an electrochemical reaction, as shown in the following equation:

[0086]

[0087] In the formula, ρ represents the lumped density of the battery; C p λ represents the lumped specific heat capacity of the battery; λ represents the lumped thermal conductivity of the battery; T represents the battery temperature; Q represents the lumped specific heat capacity of the battery. tot This indicates the total heat generation rate of the battery.

[0088] The equations for the electrochemical-thermal coupling model are:

[0089] There is a two-way coupling mechanism between the electrochemical model and the thermal model. Temperature changes affect the temperature-dependent parameters in the electrochemical model, thus forming a closed-loop feedback effect. To accurately capture this temperature dependence, the Arrhenius equation is typically used to characterize the temperature sensitivity of the physicochemical properties of lithium-ion batteries. The mathematical expression of this equation is as follows:

[0090]

[0091] In the formula, X is the temperature-sensitive parameter at the reference temperature T. ref The value below, X T E is the value of this parameter at temperature T. a,x This is the activation energy of the parameter.

[0092] After establishing an electrochemical-thermal coupled model of a lithium-ion battery, COMSOL Multiphysics was used for numerical simulation to analyze the battery's electrochemical behavior and thermal effects under different charge and discharge conditions. COMSOL Multiphysics' multiphysics coupling capability allows for the simultaneous simulation of electrochemical and thermal conduction processes. By adjusting boundary conditions and physical parameters, the simulation can obtain the current, voltage, and temperature distributions of the battery under different charge and discharge states.

[0093] Furthermore, based on the simulation results output by the electrochemical thermocoupled model under preset operating conditions and the experimental results under the same operating conditions, the deviation between the simulation results and the experimental results is calculated; the electrochemical thermocoupled model is then corrected with the deviation not exceeding a preset threshold as a constraint. In one embodiment, a 1C constant rate discharge condition at an ambient temperature of 25℃ is selected as the preset operating condition. The comparison curves of the obtained simulation results and experimental results are detailed below. Figure 3 and Figure 4 . Figure 3 The simulation and experimental results of the electrochemical-thermal coupling model under constant discharge conditions of 25℃ and 1C are shown in the figure. The maximum relative error of the terminal voltage variation curve is 4.8%. Figure 4 The simulation and experimental results of the electrochemical-thermal coupling model under constant discharge conditions of 25℃ and 1C are shown in the graph. The maximum relative error of the temperature change curve is 2.0%. Both of the above maximum relative errors are less than 6.5%, which verifies the accuracy of the electrochemical-thermal coupling model and provides a reliable basis for subsequent parameter sensitivity analysis and optimization.

[0094] S2. Latin Hypercube Sampling (LHS) and Sobol Global Sensitivity Analysis Method are used to perform global sensitivity quantification analysis on the parameters of the electrochemical thermocoupled model to obtain the sensitivity of each parameter under preset operating conditions.

[0095] The field system of the electrochemical-thermal coupling model consists of a geometric domain, a material domain, an electrochemical field, and a thermodynamic field. Key parameters are obtained through systematic analysis and screening of all parameters in the electrochemical-thermal coupling model. In this embodiment, the key parameters of the electrochemical-thermal coupling model are detailed in the table below:

[0096]

[0097]

[0098] Latin hypercube sampling uniformly divides the parameter space into multiple subspaces and randomly selects sample points from each subspace to reflect changes in model parameters while reducing errors caused by insufficient sample size. The Sobol global sensitivity analysis method decomposes the total variance V(Y) of the electrochemical-thermal coupling model output into the independent contributions of each parameter and their interaction contributions, thereby quantifying the impact of each parameter on the model output. This invention uses a first-order effect index for parameter sensitivity analysis, focusing on the core research objectives while simplifying the analysis process and ensuring the accuracy of identifying key sensitive parameters.

[0099] The specific equations mentioned above are:

[0100]

[0101] In the formula, Y(θ) represents the output of the model; θ = (θ1, θ2, ..., θ D ) represents the parameters of the model under study; V(Y) represents the total variance of the model output; S i V represents the ratio of the model's partial variance to its total variance; i V represents the one-parameter partial variance; ij This represents the partial variance of multiple parameters.

[0102] Then, by calculating the mean of the normalized first-order effect exponent of this parameter, the independent impact of each parameter on the model output was comprehensively evaluated. The specific equation is as follows:

[0103]

[0104] In the formula, S i,n S represents the first-order effect exponent; i,naverepresents the mean of the first-order effect index; m is the total number of elements of a single parameter in the normalized first-order effect index matrix under the same operating condition; T amb Indicates ambient temperature; DOD indicates depth of discharge.

[0105] Afterwards, according to S i,nave Determine the sensitivity classification of this parameter. Specifically, the sensitivity classification criteria are as follows:

[0106] If S i,nave If the value is greater than 0.4, then the parameter θ i It is a highly sensitive parameter;

[0107] If S i,nave If the value is greater than 0.2, then the parameter θ i It is a parameter of moderate sensitivity;

[0108] If S i,nave If the value is greater than 0.1, then the parameter θ i It is a low-sensitivity parameter;

[0109] If S i,nave If the above conditions are not met, then the parameter θ i It is not sensitive to the output response and is considered an insensitive parameter.

[0110] This embodiment includes three preset operating conditions: a constant 1C discharge rate at 25℃, a dynamic 0.5C-1C-2C discharge rate, and a dynamic stress test cycle automotive operating condition (DST), where C represents the charge / discharge rate. The mean value S of the normalized first-order effect exponent of the parameter pair terminal voltage and temperature rise is obtained through an electrochemical thermocoupled model. i,nave Then according to S i,nave The sensitivity classification of this parameter is determined. Furthermore, for each parameter, under a preset operating condition, the S values ​​at discharge depths of 10%, 30%, 50%, 70%, and 90% are obtained for both the terminal voltage and temperature rise. i Based on the above-mentioned S under various discharge depths i Calculate the mean S of the normalized first-order effect exponent. i,nave .

[0111] For details of the sensitivity classification results under 1C constant rate discharge conditions at 25℃, please refer to [link to relevant documentation]. Figure 5 .from Figure 5 The radius R of the positive electrode particle can be determined from this. p Positive electrode solid-phase diffusion coefficient D s,p ε, solid phase volume fraction of positive electrode s,p The negative electrode reaction rate constant k n and the radius R of the negative electrode particles n The impact on the terminal voltage is significant, while the positive electrode particle radius R pε, solid phase volume fraction of positive electrode s,p and the positive electrode solid-phase diffusion coefficient D s,p These significantly affect the average temperature rise, and are all classified as highly sensitive parameters.

[0112] For detailed sensitivity classification results under dynamic rate discharge conditions of 0.5C-1C-2C, please refer to [link to relevant documentation]. Figure 6 .from Figure 6 The solid volume fraction ε of the positive electrode can be determined from this. s,p Positive electrode particle radius R p Positive electrode solid-phase diffusion coefficient D s,p Negative electrode particle radius R n and the maximum ion concentration C at the positive electrode sma,p It significantly affects the terminal voltage, while the positive electrode solid volume fraction ε s,p , positive electrode reaction rate constant k p and the radius R of the negative electrode particles n It has a significant impact on the average temperature rise.

[0113] For details of the sensitivity classification results under dynamic stress test cyclic vehicle operating conditions, please refer to [link / reference]. Figure 7 .from Figure 7 The radius R of the negative electrode particle can be determined from this. n , positive electrode reaction rate constant k p Positive electrode particle radius R p and the negative electrode reaction rate constant k n The impact on the terminal voltage is significant, while the radius R of the negative electrode particles is... n Positive electrode solid-phase diffusion coefficient D s,p , positive electrode reaction rate constant k p Positive electrode particle radius R p Maximum ion concentration at the positive electrode C sma,p and the negative electrode reaction rate constant k n It has a significant impact on the average temperature rise.

[0114] S3, based on the sensitivity of each parameter under preset operating conditions, select a core optimization parameter group from multiple parameters for the preset operating conditions. In this embodiment, R is selected under the 1C constant rate discharge condition at 25°C. p D s,p D s,n and t + The core optimization parameter set is composed; ε is selected under dynamic rate discharge conditions of 0.5C-1C-2C. s,p C sma,p ε s,n C sin,n and C sin,p The core optimization parameter set is composed; R is selected under the dynamic stress test cycle vehicle operating condition. n k p kn C ein , λ sep and ε e,p The core optimization parameter set is described in detail below. Figure 8 .

[0115] S4. For the core optimization parameter set of the preset working condition, a non-dominated sorting genetic algorithm is used for optimization to generate a Pareto solution set with the dual objectives of minimizing terminal voltage error and temperature rise error. The Pareto solution set is then screened using the minimum Euclidean distance method, and the parameter set with the smallest distance to the ideal target point is selected as the optimal solution for the overall performance of the preset working condition.

[0116] The Non-dominated Sorting Genetic Algorithm (NSGA-II) exhibits excellent convergence performance and uniform solution set distribution. It effectively approximates the true Pareto front in complex parameter spaces, thereby obtaining an optimal parameter set that achieves a reasonable trade-off between electrical and thermal performance. Its optimization process involves randomly generating an initial population and performing non-dominated sorting to determine the dominance level of individuals. Based on this, selection, crossover, and mutation are used to generate offspring. Parents and offspring are merged, reordered, and their crowding distance is calculated. A new generation of population is then selected based on the principle of prioritizing dominance level and then crowding distance. This process iterates until a preset maximum number of generations is reached, ultimately outputting a multi-objective optimal solution set that approximates the Pareto front.

[0117] To achieve efficient execution of the aforementioned multi-objective optimization process, this invention constructs a joint simulation and optimization system architecture based on COMSOL Multiphysics and MATLAB software. COMSOL is used for numerical solution of the electrochemical-thermal coupling model, while MATLAB software serves as an external control platform to realize parameter transfer, batch simulation scheduling, and error calculation and feedback, thereby forming a complete multi-objective collaborative optimization closed-loop process.

[0118] In the specific optimization implementation process, firstly, for each preset working condition, the parameters in the core optimization parameter group under the preset working condition in step S3 are used as optimization variables for the non-dominated sorting genetic algorithm, while other parameters remain at their default settings. This effectively controls the optimization dimension and reduces the risk of overfitting. This method of selecting optimization variables comprehensively considers their sensitivity level under different working conditions, their dominant role in the bi-objective error, and the corresponding physical mechanism to ensure the rationality of the model structure and the stability of the parameter optimization results. The non-dominated sorting genetic algorithm generates an initial population within the physically feasible range of each parameter and completes multiple generations of iteration, ultimately obtaining the Pareto non-dominated solution set between the terminal voltage error and the temperature rise error under the corresponding working condition. This solution set characterizes the trade-off between the model's electrical performance and thermal performance prediction accuracy. To select a representative set of optimal parameters from the Pareto solution set for subsequent model validation, the minimum Euclidean distance method is introduced as the solution set selection criterion, selecting the solution with the smallest distance from the ideal point as the optimal solution in terms of overall performance. By comparing and analyzing the convergence of the objective function, the trend of error change, and the characteristics of the Pareto solution set under different operating conditions, the improvement effect of the model's fitting ability in the dual objective dimensions of terminal voltage and temperature rise can be comprehensively evaluated. Figure 9 The optimal solution for comprehensive performance is substituted into the electrochemical thermocoupled model under three preset operating conditions. The optimized back-end voltage and temperature rise data are output and compared with the simulation data and experimental data before optimization. Figure 9 The diagram shows a comparison of the terminal voltages under a constant 1C discharge condition at 25℃. Figure 10 The figure shows a comparison of temperature rise under 1C constant rate discharge conditions at 25℃. Figure 11 The diagram shows a comparison of the terminal voltages under dynamic rate discharge conditions of 0.5C-1C-2C. Figure 12 The diagram shows a temperature rise comparison under dynamic rate discharge conditions of 0.5C-1C-2C. Figure 13 The diagram shows a comparison of the terminal voltages under cyclic vehicle operating conditions during dynamic stress testing. Figure 14 A comparison graph showing the temperature rise under dynamic stress test cycle conditions in vehicles is presented.

[0119] Furthermore, to intuitively quantify the optimization effect, mean square error (MSE) was introduced for error analysis. The changes in terminal voltage MSE and temperature rise MSE before and after optimization under three typical operating conditions were systematically summarized. Detailed data are as follows: Figure 15 and Figure 16As shown, under a constant 1C discharge condition at 25℃, the voltage error is reduced by approximately 79.5%, and the temperature rise error is reduced by approximately 7.8%. Under a dynamic discharge condition of 0.5C-1C-2C, the voltage error is reduced by approximately 29.2%, and the temperature rise error is reduced by approximately 45.4%. Under dynamic stress test cycle automotive conditions, the voltage error is reduced by approximately 58.3%, and the temperature rise error is reduced by approximately 10.3%. Overall, the optimization strategy has achieved significant results in both voltage and temperature rise prediction, especially in improving voltage fitting accuracy. The optimization strategy demonstrates excellent performance, particularly in variable discharge rates and automotive conditions.

[0120] S5 constructs a general parameter combination based on the optimal comprehensive performance solution under various preset working conditions.

[0121] After optimizing the parameters under three preset operating conditions, this embodiment further integrates the optimal comprehensive performance solutions obtained under the three preset operating conditions to construct a set of general parameter combinations for model validation. This general parameter combination is directly formed by summarizing the optimal comprehensive performance solutions obtained from the optimization of the three preset operating conditions. It focuses on covering the highly sensitive and moderately sensitive physical parameters in the electrochemical-thermal coupling model that have a dominant influence on terminal voltage and temperature rise response, while all low-sensitivity and insensitive parameters remain at their default settings. This ensures that key parameters are fully optimized while effectively controlling the overall parameter dimension, reducing redundant adjustments and overfitting risks, and maintaining the stability of the model structure and physical meaning. After constructing the general parameter combination, it is applied to the electrochemical-thermal coupling model to conduct multi-condition applicability verification. Considering the relatively stable electrochemical process and thermal response characteristics of the battery under 1C constant rate conditions, it is selected as the standard verification condition to test the prediction accuracy and adaptability of the general parameter combination under standard load conditions. For details, see the comparison of the predicted terminal voltage and temperature rise results and experimental data of the model before and after optimization under 1C constant rate conditions. Figure 17 and Figure 18 The results show that the model's prediction performance is significantly improved after adopting a unified parameter combination. The mean square error of the terminal voltage prediction is reduced by 93.8%, the temperature rise prediction error is reduced by 75.5%, and the prediction curves show good consistency with the experimental data. In summary, the integrated method of parameter sensitivity quantification and multi-objective collaborative optimization proposed in this invention realizes full-process control of lithium-ion battery electrochemical-thermal coupling model parameters, from accurate quantification of sensitivity under multiple operating conditions and dual-objective collaborative optimization to unified parameter construction and verification. This significantly improves the model's prediction accuracy, reliability, and engineering applicability under different operating conditions.

[0122] In summary, this invention deeply integrates a multi-condition global sensitivity quantification method based on Latin hypercube sampling and the Sobol exponent method with the NSGA-II multi-objective optimization algorithm. This constructs an integrated optimization method for electrochemical-thermal coupled model parameters, covering parameter sensitivity analysis, dual-objective collaborative optimization, and cross-condition verification. This achieves closed-loop control of the entire process of lithium-ion battery model parameters, from full-field screening and hierarchical quantification to simultaneous improvement of terminal voltage and temperature rise prediction performance. This method can systematically identify and hierarchically screen multiple key parameters, including geometric, capacity, transport, kinetic, and thermodynamic parameters, overcoming the problems of incomplete parameter coverage and one-sided sensitivity identification caused by single operating conditions in existing technologies. Simultaneously, through the dual-objective optimization framework of terminal voltage and temperature rise, it effectively balances the accuracy of electrochemical performance prediction with the requirements of thermal safety control, breaking through the performance bottlenecks of traditional single-objective optimization and multi-objective imbalance. Furthermore, relying on the closed-loop mechanism of "sensitivity quantification - hierarchical optimization - cross-condition verification", the sensitivity analysis results provide accurate guidance for the optimization process and stable adaptation of optimization parameters under multiple operating conditions. This significantly reduces model prediction bias and improves the prediction accuracy, reliability, and applicability of the model in complex operating scenarios such as constant rate, variable rate, and dynamic load. It provides efficient, universal, and engineering-feasible technical support for battery state estimation and thermal safety management in fields such as new energy vehicles and energy storage systems.

[0123] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for quantifying and optimizing the sensitivity of parameters in a lithium battery electrochemical-thermal coupling model, characterized in that, Includes the following steps: S1, Construct an electrochemical-thermal coupling model for lithium batteries; S2, using Latin hypercube sampling and Sobol global sensitivity analysis, the parameters of the electrochemical thermocoupled model are subjected to global sensitivity quantification analysis to obtain the sensitivity of each parameter under preset operating conditions; S3, based on the sensitivity of each parameter under preset working conditions, select a core optimization parameter group from multiple parameters for the preset working conditions; S4. For the core optimization parameter set of the preset working condition, the non-dominated sorting genetic algorithm is used for optimization to generate a Pareto solution set with the dual objectives of minimizing terminal voltage error and temperature rise error. The Pareto solution set is then screened using the minimum Euclidean distance method, and the parameter set with the smallest distance to the ideal target point is selected as the optimal solution for the overall performance of the preset working condition. S5 constructs a general parameter combination based on the optimal comprehensive performance solution under various preset working conditions.

2. The method for quantifying and optimizing the sensitivity of parameters in a lithium battery electrochemical-thermal coupling model according to claim 1, characterized in that, Step S1 includes the following steps: The electrochemical-thermal coupling model includes a geometric field, a capacity field, a transport field, a kinetic field, and a thermodynamic field.

3. The method for quantifying and optimizing the sensitivity of parameters in a lithium battery electrochemical-thermal coupling model according to claim 2, characterized in that, Step S1 also includes the following steps: Based on the simulation results output by the electrochemical thermocoupled model under preset operating conditions and the experimental results under the same operating conditions, the deviation between the simulation results and the experimental results is calculated. The electrochemical thermocoupled model is modified under the constraint that the deviation does not exceed a preset threshold.

4. The method for quantifying and optimizing the sensitivity of parameters in a lithium battery electrochemical-thermal coupling model according to claim 1, characterized in that, Step S2 includes the following steps: Obtain the ratio of the partial variance to the total variance of the electrochemical-thermal coupling model for multiple discharge depths under preset operating conditions; The mean of the normalized first-order effect index of the parameter is determined based on multiple ratios. The sensitivity category of the parameter under preset operating conditions is determined based on the mean value.

5. The method for quantifying and optimizing the sensitivity of parameters in a lithium battery electrochemical-thermal coupling model according to claim 4, characterized in that, "Determining the sensitivity category of the parameter under preset operating conditions based on the mean value" includes the following steps: When the mean value is greater than the first preset value, the sensitivity category of the parameter is high sensitivity; When the mean value is less than a first preset value and greater than a second preset value, the sensitivity category of the parameter is moderately sensitive. When the mean value is less than the second preset value and greater than the third preset value, the sensitivity category of the parameter is low sensitivity; When the mean is less than a third preset value, the sensitivity category of the parameter is insensitive. The first preset value is greater than the second preset value, and the second preset value is greater than the third preset value.

6. The method for quantifying and optimizing the sensitivity of parameters in a lithium battery electrochemical-thermal coupling model according to claim 1, characterized in that, The preset operating conditions include a constant 1C discharge condition at 25°C, a dynamic discharge condition ranging from 0.5C to 1C to 2C, and a dynamic stress test cycle for vehicles.

7. The method for quantifying and optimizing the sensitivity of parameters in a lithium battery electrochemical-thermal coupling model according to claim 6, characterized in that, Step S4 includes the following steps: Based on the simulation and experimental results of the optimal solution for overall performance under preset operating conditions, determine whether it is necessary to optimize the optimal solution for overall performance.

8. The method for quantifying and optimizing the sensitivity of parameters in a lithium battery electrochemical-thermal coupling model according to any one of claims 1-7, characterized in that, Step S5 includes the following steps: Based on the simulation and experimental results of the general parameter combination, determine whether the general parameter combination needs to be optimized.

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